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This just remembered me of an old famous song for children....
"Era uma casa muito engraça, / It was a very funny house,
não tinha teto, não tinha nada. / It had no ceiling, it had nothing.
Ninguém podia entrar nela não / No one could get inside it
porque na casa não tinha chão. / because in the house there was no floor.
Ninguém podia dormir na rede / No one could sleep in the hammock
porque na casa não tinha parede. / because in the house there were no walls.
Ninguém podia fazer pipi / No one could take a leak
porque penico não tinha ali. / Because there was no pot in there.
Mas era feita com muito esmero, / But it was very diligently built,
na Rua dos Bobos, número zero." / On the Street of the Silly, number zero.
In "dancing around my head" it's "em volta da".
You're circling something.
Or maybe, if you really don't intend "circling", you can use "na". There is no exact path, but it's still your head. (May be seen as "dancing around in my head").
Check some examples of "por aí", which is a completely indefinite location:
- Te vejo por aí = See you around
- Vou andar por aí = I'll take a walk / I'll walk around
- Q: Cadê o gato? Ans: (Es)tá por aí.... = Where's the cat? It must be around somewhere....
"Por aí" comes from something a little more literal using "por + location", where "por" is a vague movement and "aí" is a vague location, making "por aí" totally vague.
- A formiga anda pela (por+a) mesa = The ant walks around on the table
- A menina corre pelo (por+o) apartamento = The girl runs around inside the apartment